Here is what I came up with:

Public Sub SeqDate()

Dim lngBottomRow As Long
Dim blnContinue As Boolean

blnContinue = True

Do Until blnContinue = False
    lngBottomRow = ActiveSheet.Range("A65536").End(xlUp).Row
    blnContinue = False
    For i = 2 To lngBottomRow
        If ActiveSheet.Cells(i, 1).Value - ActiveSheet.Cells(i - 1, 1).Value > 1 Then
            ActiveSheet.Rows(i).Insert shift:=xlShiftDown
            ActiveSheet.Cells(i, 1).Value = ActiveSheet.Cells(i - 1, 1).Value + 1
            ActiveSheet.Cells(i, 2).Value = WeekdayName(Weekday(ActiveSheet.Cells(i, 1).Value))
            blnContinue = True
        End If
    Next i
Loop

End Sub